Welcome to the site. Your question concerns a common topic that has been extensively covered here: Is it naive to tell my current employer that I'll be leaving, months in advance?. I feel like the answers on that question reliably argue the pros and cons of giving more than the standard amount of notice. In the end it comes down to how your employer will react which you can base on how they reacted in the past to people leaving.
– Lilienthal♦Apr 19 '16 at 17:52

I haven't voted to close this as a duplicate of that question as while I think it covers your situation sufficiently, I can see an argument being made for your question being different from the general case. I've had a search for related questions about an upcoming business trip or training but found no matches.
– Lilienthal♦Apr 19 '16 at 17:54

I would mention that when asking questions that are particular to a certain country or region (such as notice periods) it's advisable to note that in the tags (such as India or UK, for example).
– Chris EApr 19 '16 at 17:57

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You may have a good relationship with your boss, but he is still your boss, and not your friend. If you tell him that you plan to leave you might find that it's better for your boss to get rid of you ASAP, rather than allow you to take your time for another month. Consider the possible implications before you say something that could be used against you.
– AndreiROMApr 19 '16 at 19:42

Is this training something that won't be potentially useful for you in the future?
– KilisiApr 19 '16 at 19:43

1 Answer
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Not sure if it's different in the UK, but in the US you can be released prior to your notice period. If you are prepared to be escorted out of the building the moment you give notice, and it will make no difference in your outlook or plans, then there's no harm in giving additional notice in hopes of sparing your employer the expense of training.

On the other hand:

Things change for the worse all the time. Giving notice only when you have to is a kind of insurance against financial disaster.

Could the training be beneficial to you in the future? As an employee in good standing, you have in a sense earned the right to this training, based on your previous effort.

It's a cost of doing business to train employees who will not stay with the company. It's rare to stay in one job your entire career, so it's expected that some who are trained will in fact move on.

I would argue that there's always too much risk involved to give additional notice, and the employer is always in a better financial position to absorb any loss associated with an employee's departure.

I would be surprised if most employers made decisions on the basis of the cost incurred by an employee upon being unemployed.

Generally, in the US, if they release you prior to your notice period, you've now been fired (as opposed to resigning) and they have to pay unemployment benefits. I have often seen that they may show you the door for security/IP reasons, but still pay you through your notice period to avoid dealing with unemployment. Obviously the length of the notice period can be a deciding factor.
– cdkMooseApr 19 '16 at 21:07